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I'm reading a book where the autocorrelation of white noise is expressed as:

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What is the term $Q(k)$ and why is is expressed as an average value of a dot product ?

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    $\begingroup$ That's not an average, that's an expectation operator! Anyway, that's really a topic for a different day. $Q$ is probably just the covariance matrix, and it's likely defined somewhere around this? $\endgroup$ – Marcus Müller Feb 9 at 10:03
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I’m guessing your book is on Kalman filters and $u(k)$ is a term in a state variable equation of a linear system. If so, it is a vector and the components of that vector at some time index $k$ can be correlated with each other but are independent with respect to $k$.

it isn’t a dot product, it is an outer product.

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